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From: Tim Golden BandTech.com on 28 May 2010 11:00
On May 27, 5:44 pm, zookumar yelubandi <zooku...(a)yahoo.ca> wrote:
> On Wed, 26 May 2010 04:30:39 -0700 (PDT), Tim Golden BandTech.com wrote:
> > On May 26, 12:07 am, Thomas Heger <ttt_...(a)web.de> wrote:
> [...]
> >> Interesting question would be, what would happen, if that is not seen by
> >> us, but with a timeline in an angle - say perpendicular. That is a kind
> >> of multiverse picture, where our matter is radiation and our time is a
> >> spatial axis. That doesn't need to be far away, but could be 'round the
> >> corner'.
>
> >> Greetings
>
> >> Thomas
>
> > I can only half follow what you are describing, but I do see that you
> > are exercising a recurrent phenomenon. When you step up to a bi-
> > quaternion aren't you now in an 8D work space?
>
> > As you are thinking in terms or rotation quite a bit, then this is a
> > fine area of primitive mathematics to focus on.
>
> > Can one object have several axes of rotation? Here Euler angles would
> > have one thing to say, but can we already accept that even within 3D
> > that there are multiple axes? Let's say I spin a top aligned
> > vertically here at roughly 43 degrees north latitude. This top may be
> > spinning relative to me at, say, 600 rpm. Is it also spinning about
> > the earths rotational axis at 6.9E-4 rpm? Experiment and math will
> > tell us that it will not. But what about in higher dimension? If we're
> > going to worry about the 'axes' of the electrons in the spinning top
> > then we'll have to admit that we've caused precessionary forces. What
> > about in the atomic nuclei?
>
> Can there be multiple rotational axes as long as they reside outside the
> body of the object? The question of the nuclei wouldn't arise (??? )then
> because the group can rotate together about any number of external axes
> (but about only one internal axis at any one time). Here, each successive
> larger axis of rotation must absorb the entire orbit of rotation about the
> preceding smaller axis. In effect, the smaller orbit itself becomes the
> object of rotation about the larger axis. Let me get a cup of coffee.
> My brain wants to really believe this; but whenever that happens, I know
> it's a trap. ;)

Well, I am this way too. A gyroscope's behavior tells us that this
'multiple axes of rotation' will not exist. Even without all that
freedom a bike wheel spinning in our hands tells us 'no'. Then coming
down to math, what do we have? We can give up mass at this level, and
if we want to discuss a solid object and its many possible
orientations then we have no problem, but when we attemp to
superimpose two simultaneous rotational axes onto one object I believe
we witness a noncomuttative property. I may stand to be corrected
here, but I'll try to expound on why I think that this is so.

In order to even declare a single rotational axis on an object we will
be forced to select two point positions (for a three dimensional
object) as forming the axis, and to specify a distict amount of
rotation we might take a third point and expose it's traverse.

To declare a second rotation we should repeat the steps of the first
selection, but with unique points. These then are two independently
defined rotational axes, each acceptable on its own terms.

If we perform the first rotation, then perform the second rotation
then we should witness the object's traverse over those discrete
rotations.

When we perform the second rotation then the first rotation we witness
a new position different from the first commutation of the operation.

I am reasonably comfortable verifying this with a mug with a handle on
it here at my desk, performing two 90 degree rotations.

>
> Thinking about this longer, doesn't rotation imply restoration? Can
> precessionary forces involving multiple axes ever restore a point such that
> we can measure its periodicity?
>
> One question begets another.
>
> Just thinking out loud ... say you have a solid sphere. Spin it about the
> Y-axis. Simultaneously, spin it about the X-axis. Can this be done
> without changing the fixed relation of the sphere's composing atoms?
> My intuition says no. Which is why I propose that multiple axes of spin
> can only be achieved if the axes reside outside the body of the object;
> moreover, that successive imparted spins must involve the entire orbit of
> the previous imparted spin. It's a tad abstract.

Hmmm. To define the spin on an object from outside carefully would be
helpful.
Above I've tried it in a way that is coherent to the object. Anyway,
these exercises are free aren't they? If you wound up with a coherent
model of how that sphere's 'atoms' rearranged themselves you could
well wind up with a new theory of atoms. Whether to remain in the
physical or recover the physical from a seemingly ambiguos
definition... I'd try for the latter, but have a hard time getting
away from the former.

>
> Then there's the circular saw. You can turn it on its natural axis and
> cut yourself a nice piece of lumber, but if you place the next spin axis
> anywhere where it intersects any part of the blade's peripheral orbit ...
> watch out.

Nice, and we do actually have the ability to control the orientation
of that saw with a good amount of freedom, though the forces involved
may be a bit trickier than we realize when doing that. It's not as if
we're caught in a precession that will not end, cutting aside. Thanks
Zook.

- Tim

>
>
>
> > Somehow I still feel satisfied that there can be many rotational axes,
> > and that all of matter can be in such a dizzying rotational flux, and
> > that we have no sense of it because all that is around us is in
> > similar flux. I've actually had this as an intense sensation before
> > and it was memorable. It is a bit chaotic and I don't mean to validate
> > it by this means, just trying really to go toward some simple math.
> > It is possible to constrain to a purely rotational system, by fixing
> > all positions to a unit radius within a 4D Euclidean space. One could
> > call this a unified theory from the get go, because of the unity
> > distance constraint. What is left is 3D freedom, but no access to the
> > origin. All of this 3D freedom is expressible in angular quantities,
> > yet there is not necessarily any distinction from standard space,
> > except over long distances, where it should be possible to travel in
> > one direction and land back at yourself again. Wouldn't it be a grand
> > chuckle if all those galaxies were just prior versions of us in a
> > kaleidoscopic array? This then would lead us to believe that we are
> > existent in a pocket of well behaved space, for the vast open
> > territory never populated. This is anathema to Einstein's postulate,
> > but I see no problem with it. Space is not the same in all directions.
> > I look left and I see a chair. I look right and I see a bucket. This
> > is sufficient evidence to observe that space is not the same in all
> > directions.
>
> > Rotation is an awfully pretty concept. That it might be defined in
> > terms of translation is just one way to look at things. Translation
> > can also be looked at as rotation. We've been programmed to work from
> > the Euclidean basis, at least I have, and I wish that I could make
> > more sense of the unified rotational approach. Anyway, it's exercise.
> > The 'multiple axis problem' is what I see.
> > - Tim
>
> Yes, very interesting stuff.
>
> Uncle Zook

From: spudnik on 28 May 2010 17:25
as Tim LocquaciousHand implies,
"composition" of two rotations, one after the other,
is not commutative, as the demonstration also can
be modeled with quaternion multiplications; in any case,
two roatations resolve into one, about a different axis.

the question is,
if you try to do them simultaneously,
what happens?

and, please, see if you can show it with quaternions,
instead of this interminable blabfest; thank *you*.

thusNso:
Dear woould-be replacer of Jerry "no oil, except from Texas etc."
Brown:
no change from Jerry Brown's '69 "platform," eh?
it is intolerably stupid, insofar as we do
need "fossilized fuels TM (sik),"
to not get our share from our own "reserves." really, though,
it is merely biomass, and the techniques have progressed since '69.
Dubya's bro's ban offshore of Florida (and Louisiana) seemed like
a tactical maneuver to support the oilcos' scarcity programme
in our state. (why O why O why do folks believe,
that the oilcos did not support the Kyoto Protoccol,
which was just another cap'n'trade "free trade" nostrum,
that Dubya'd have undoubtdely signed, if he had been told?)
British Petroleum, the balls-out advocate of cap'n'trade,
"Beyond Petroleum," is also the biggest company
in the Alaska North Slope -- doesn't any body wonder,
why no-one asked Palin about her BP-employed hubbie, and
his Seccesionist ideals?
one must take into consideration, with all of the hype about it,
that oil comes out of the ground underwater in "seeps,"
under pressure. so, how much would come out, if
BP et al ad vomitorium were not pumping like crazy?
Waxman's current cap'n'trade bill just mandatorizes the huge,
voluntary cap'n'trade since 2003 -- tens of billions
in hedging per annum. what the Liberal Media (Ownwd
by consWervative) don't talk about, is that
he brought the first cap'n'trade bill in '91,
under HW (who worked with Gore on the Kyoto cap'n'trade).
what it amounts to, as Waxman basically admitted to,
when he was at UCLA, is "let the arbitrageurs raise the price
of energy, as much as they can in the 'free market' --
free beer, freedom!"
a small, adjustable carbon tax would achieve the same ends
-- as I even read "in passing" in a guest editorial in the WSUrinal,
as well as from an "expert" in a UCLA seminar, but who said that
it was (some how) "politically impossible" --
without being the Last Bailout of Wall Street (an
the City of London).

thusNso:
I never read a word about Palin's hubbie's Seccesh "movement"
in the Liberal Media (Owned by consWervatives) and
that is sort-of the issue in AZ. I'm all for kids whose parents
managed to sneak
across the border & give birth, but I was taken aback
by the "sense of entitlement" that the older kids have, about college
(the DREAM Act; I stated to a group of them, that
crossing the border is essentially a Mexican "rite of passage," and
it is certainly not very dangerous as a proper hike, if
you check the FAQs and maps & so forth
from the Mexican goment (and those advocacy/
haven groups in the USA; it may be difficult in the summer,
though). well, it's either that or college *in* Mexico, or
you'll probably be made to join a gang.
La Raza d'Atzlan are openly racist, not just by their title; at
least,
that's the impression that I got, attending one of their meetings
at UCLA, two or three years ago -- it's in their God-am constitution.
of course, teh real problem is "free trade," and
this is already here to roost;
the little spill in the Gulf is being used by British Petroleum
-- which is also the #1 driller
in the Alaska North Slope,
that Ted Palin works for --
to create an "outsourcing" mandate to solve the problem, because
we can't do it with our post-industrial cargo cult. well, iscrew
that!
read LaRouche, if you want to know the history with Lincoln
and his "Spot Resolutions;"
Cinco de Mayo should be a pan-american holiday!

--Light: A History!
http://wlym.com
From: J. Clarke on 31 May 2010 09:34
On 5/27/2010 4:55 PM, Thomas Heger wrote:
> Tim Golden BandTech.com schrieb:
>> On May 26, 11:10 am, Thomas Heger <ttt_...(a)web.de> wrote:
>>> Tim Golden BandTech.com schrieb:> On May 26, 12:07 am, Thomas Heger
>>> <ttt_...(a)web.de> wrote:
>>>>> Tim Golden BandTech.com schrieb:> On May 23, 2:34 am, Thomas Heger
>>>>> <ttt_...(a)web.de> wrote:
>>>> I can only half follow what you are describing, but I do see that you
>>>> are exercising a recurrent phenomenon. When you step up to a bi-
>>>> quaternion aren't you now in an 8D work space?
>>> This is the trouble with the term 'dimension'. If we talk about space in
>>> an euclidiean way, we mean something like the distance to remote
>>> objects, where the objects inhabit a certain position.
>>> These positions are based on a certain view (ours!), because this is how
>>> we do it. The distance is measured in light-years and we use a vector
>>> space to put those distances in.
>>> But: the space we observe is dependent on us, because we have the
>>> dependency on time, because distance means age, too. Than our vision
>>> cannot be something 'real', but is specific to our position and
>>> movement.
>>> What is real than? Well, that is the question. If euclidean space is
>>> where we would see the objects, than that is not where they are now.
>>> The concept of distance seems useful, so we could assume some kind of
>>> space with dimensions of type distance, that is mainly invisible. We
>>> could see it only in the direct vicinity. And we have relativity, that
>>> needs timelines in various directions (to enable the objects to move).
>>> Than we would expect direct contact to be possible and empty space to
>>> move within.
>>> But if we alter the timeline, space seem to contract and a new space
>>> appears, unseen before. This could be achieved, if the axis is expanding
>>> to a circle and the former circumference contracts to an axis.
>>> This could be modeled with bi-quaternions by flipping the picture to the
>>> side and exchange timelike and spacelike.
>>> If we multiply two bi-quaternions 'sideways' (the spacelike neighbors),
>>> there would appear a scalar part, a vector part (with three dimensions
>>> of type length) and a cross-product term. If the cross-product term is
>>> actually responsible for material objects, the relations could be
>>> exchanged and material objects turn into radiation and vice versa. But
>>> we have still a vector space with three dimensions of type length, only
>>> another one. Since left and right turns into before and after, the
>>> timeline is altered and causal relations change from simultaneous to one
>>> after the other.
>>> Even if this sounds strange, it would be consistent with GR.
>>>
>>>> As you are thinking in terms or rotation quite a bit, then this is a
>>>> fine area of primitive mathematics to focus on.
>>>> Can one object have several axes of rotation? Here Euler angles would
>>>> have one thing to say, but can we already accept that even within 3D
>>>> that there are multiple axes?
>>> The 'trick' - if you like - is, that the axis are for different spheres
>>> of different size. Any such sphere has only one, but they are connected
>>> in a specific manner like the one called Descartes configuration.
>>>
>>>> Let's say I spin a top aligned
>>>> vertically here at roughly 43 degrees north latitude. This top may be
>>>> spinning relative to me at, say, 600 rpm. Is it also spinning about
>>>> the earths rotational axis at 6.9E-4 rpm? Experiment and math will
>>>> tell us that it will not. But what about in higher dimension? If we're
>>>> going to worry about the 'axes' of the electrons in the spinning top
>>>> then we'll have to admit that we've caused precessionary forces. What
>>>> about in the atomic nuclei?
>>> Well, we have inertia to be explained. A rotational paradigm in
>>> spacetime would perfectly fit (in my eyes), because more spin would make
>>> things more stable and that spin could be related to energy or mass.
>>> Energy more for things that change and mass for stability. And we could
>>> see why and how both be converted.
>>> (Than matter is kind of 'wrapped up light'.)
>>
>> Within the unit shell model (constrain distance to unity in nD to
>> yield n-1D space) this makes tremendous sense, though the possibility
>> of reverse spin modes would suggest some dynamics. Picture rotational
>> axes in toward the origin from the shell, then this direction is
>> nonobservable from a shell constrained object. This is a Flatland
>> interpretation. Anyway, the ordinary principle of rotational moment
>> are not necessarily to be upheld within this paradigm. Rather it
>> should be recovered as an extension of the paradigm, and preferably
>> from simpler principles, or principles that yield more consequents
>> than just mass. I don't think that the nonobservable concept is
>> complete, and that is good, since we would like to witness
>> interactions if we are elements of that shell. Stability as you
>> mention is a good thing to consider. This makes me ponder the vortex
>> models that some are fond of. You like those right? There are some
>> problems with this model, but they are there for all models. The
>> puzzle is what to grant and how slight can the grant be?
>>
>> For me I would like to try to adapt polysign into this space, but I'm
>> not seeing it too well just yet.
>
> Hi Tim
> of course I wanted to model vortices.

It is very difficult to imagine you having the mathematical background
to model vortices. How many years of math have you had anyway?
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